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P.T.O.
MAR IVANIOS COLLEGE (AUTONOMOUS)
THIRUVANANTHAPURAM
Reg. No. :.………………… Name:………………….
Fourth Semester B.Voc. Degree Examination, June 2016
First Degree Programme under CSS
General Course (for Software Development)
AUSD461: Mathematics II
Time: 3 Hours Max. Marks: 80
SECTION A
Answer ALL questions in one or two sentences.
1. Give a counter example for the statement "All natural numbers 2 are prime".
2. Define simple path.
3. When a relation is said to be an equivalence relation.
4. Define ordered set.
5. Give an example for a group.
6. What is the characteristic function of a set
7. If A and B then A B ...........
8. Define a Fuzzy relation.
9. Fallacies means
10. Define automation.
(10 1 10 Marks)
SECTION B
Answer any EIGHT questions, not exceeding a paragraph of 50 words.
11. Define a graph and give one example.
12. Define a binary operation on a set.
13. Explain inductive proof and false proof.
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14. Prove that → ≡ p ¬q.
15. Define a group and illustrate with an example.
16. Define a partially ordered set and give one example.
17. Give an example for recursively defined function.
18. Let A and B c}. If
R then find R-1.
19. Let G be a group and let c be elements of then prove that ab ac ⇒ b c.
20. Define Fuzzy subset and support of a Fuzzy subset.
21. Define an integral domain.
22. Define cycles and give an example for a directed acyclic graph.
2 16 Marks)
SECTION C
Answer any SIX questions, in a page of 100 words.
23. Prove that p and q are logically equivalent.
24. Give the truth table for biconditional.
25. Define ring and give one example.
26. When a group is said to be abelian. Give one example.
27. Let A and B 11, 9}. Find A A B and A × B.
28. Prove that
2

1


n n
n i n
i .
29. Prove that → ⇔ A → → is a tautology.
30. Give a note on composition of relations.
31. Give any four types of relations.
4 24 Marks)
SECTION D
Answer any TWO questions, not exceeding four pages.
32. If is a ring with additive identity 0 and b ∈ then prove the following
a). 0.a a.0 0
b). a b
c). ab
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ii). Let G be a group of real numbers under addition and G-1 be the group of
positive real numbers under multiplication. Define G → G-1 by ex.
Then prove that f is an isomorphism.
33. Prove that 2 is irrational. Prove that in a group, the identity element is
unique.
34. State and prove De Morgan's laws for sets.
35. Explain the Depth First search algorithm.
15 30 Marks)